Vibration Control of Offshore Wind Turbine Towers Based on Eddy Current Nonlinear Energy Sink

doi:10.16182/j.issn1004731x.joss.25-0660

Abstract

Abstract:

To address the issue of tower vibrations induced by wind loads, which can damage the structure of wind turbines, a vibration control method for monopile offshore wind turbine towers based on an eddy current-nonlinear energy sink (EC-NES) was proposed. The dynamic model of monopile offshore wind turbines based on EC-NES was constructed according to the Euler-Lagrange equation, and based on the output response of FAST software, the unknown parameters of the model and the wind loads were identified in terms of parameters. The optimal parameters of EC-NES stiffness and damping were obtained using PSO. The eddy current damper was designed based on these optimization results. The simulation results have shown that compared with traditional tuned mass dampers, the EC-NES device can effectively suppress the deflection angle of wind turbine towers, and it shows stronger robustness to the frequency change of the main structure.

Key words: offshore wind turbine, structural damping, nonlinear energy sink, eddy current, PSO algorithm

CLC Number:

TP391.9

Yu Xiangxing, Zhao Yandong, Zhang Baolin. Vibration Control of Offshore Wind Turbine Towers Based on Eddy Current Nonlinear Energy Sink[J]. Journal of System Simulation, 2025, 37(12): 3007-3017.

Figures/Tables 21

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Table 1

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Table 2

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Table 3

Parameters of 5 MW monopile offshore wind turbine model

参数	参数值
$m t$ /kg	$929 397$
$d t$ $/ (N ⋅ m ⋅ s / r a d)$	$7.69 × 107$
$I t / (k g ⋅ m 2)$	$4.30 × 109$
$k t / (N ⋅ m / r a d)$	$2 × 1010$
$R t / m$	$67.997$
$R n / m$	$107.6$

Table 3

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Table 4

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References 19

[1]	Dai Kaoshan, Huang Hai, Lu Yang, et al. Effects of Soil-structure Interaction on the Design of Tuned Mass Damper to Control the Seismic Response of Wind Turbine Towers with Gravity Base[J]. Wind Energy, 2021, 24(4): 323-344.
[2]	Zhang Yun, Wang Yilong, Zhao Yandong, et al. Observer-based Model Reference Adaptive Control for Offshore Wind Turbines Subjected to Wind and Wave Loads[J/OL]. Transactions of the Institute of Measurement and Control. (2025-04-01) [2025-09-09]. .
[3]	Ding Hao, Bi Kaiming, Song Jian, et al. Vertical Vibration Control of Structures with Tuned Liquid Column Dampers[J]. International Journal of Mechanical Sciences, 2024, 279: 109502.
[4]	Reiterer Michael, Muik Joachim. Application of Parametric Forced Tuned Solid Ball Dampers for Vibration Control of Engineering Structures[J]. Applied Sciences, 2023, 13(12): 7283.
[5]	Bian Jing, Jing Xingjian. Superior Nonlinear Passive Damping Characteristics of the Bio-inspired Limb-like or X-shaped Structure[J]. Mechanical Systems and Signal Processing, 2019, 125: 21-51.
[6]	Wang Yu, Jing Xingjian. Nonlinear Stiffness and Dynamical Response Characteristics of an Asymmetric X-shaped Structure[J]. Mechanical Systems and Signal Processing, 2019, 125: 142-169.
[7]	Zhang Wenxue, Zhang Cheng, Su Lijun, et al. Experimental Study on the Dynamic Performance of a Winding Rope Fluid Viscous Damper[J]. Engineering Structures, 2023, 281: 115786.
[8]	Liang Chen, Yuan Yong, Yu Xiaotao. Applying New High Damping Viscoelastic Dampers to Mitigate the Structural Vibrations of Monopile-supported Offshore Wind Turbine[J]. Ocean Engineering, 2024, 295: 116910.
[9]	Aliakbari Fatemeh, Garivani Sadegh, Ali Akbar Aghakouchak. An Energy Based Method for Seismic Design of Frame Structures Equipped with Metallic Yielding Dampers Considering Uniform Inter-story Drift Concept[J]. Engineering Structures, 2020, 205: 110114.
[10]	Theurich Timo, Gross Johann, Krack Malte. Effects of Modal Energy Scattering and Friction on the Resonance Mitigation with an Impact Absorber[J]. Journal of Sound and Vibration, 2019, 442: 71-89.
[11]	陈政清, 黄智文, 王建辉, 等. 桥梁用TMD的基本要求与电涡流TMD[J]. 湖南大学学报(自然科学版), 2013, 40(8): 6-10.
	Chen Zhengqing, Huang Zhiwen, Wang Jianhui, et al. Basic Requirements of Tuned Mass Damper for Bridges and the Eddy Current TMD[J]. Journal of Hunan University(Natural Sciences), 2013, 40(8): 6-10.
[12]	练继建, 赵悦, 练冲, 等. 基于电涡流-调谐质量阻尼器的海上风电筒型基础结构减振研究[J]. 振动与冲击, 2019, 38(19): 20-25.
	Lian Jijian, Zhao Yue, Lian Chong, et al. Vibration Reduction of Offshore Wind Turbine Tube Infrastructures Based on EC-TMD[J]. Journal of Vibration and Shock, 2019, 38(19): 20-25.
[13]	Lian Jijian, Zhao Yue, Lian Chong, et al. Application of an Eddy Current-tuned Mass Damper to Vibration Mitigation of Offshore Wind Turbines[J]. Energies, 2018, 11(12): 3319.
[14]	陈舒坪. 电涡流非线性能量阱的控制机理及减震设计研究[D]. 广州: 广州大学, 2022.
	Chen Shuping. Study on Control Mechanism and Seismic Reduction Design of Eddy-current Nonlinear Energy Sink[D]. Guangzhou: Guangzhou University, 2022.
[15]	Dou Jinxin, Yao Hongliang, Cao Yanbo, et al. Performance Improvement of NES Based on Eddy Current Damping[J]. Mechanical Systems and Signal Processing, 2023, 188: 109994.
[16]	Jonkman J, Butterfield S, Musial W, et al. Definition of a 5-MW Reference Wind Turbine for Offshore System Development[EB/OL]. [2025-05-16]. .
[17]	Jonkman J M. Dynamics Modeling and Loads Analysis of an Offshore Floating Wind Turbine[EB/OL]. [2025-05-16]. .
[18]	陈政清, 黄智文. 一种板式电涡流阻尼器的有限元模拟及试验分析[J]. 合肥工业大学学报(自然科学版), 2016, 39(4): 499-502.
	Chen Zhengqing, Huang Zhiwen. Finite Element Simulation and Experimental Test of a Plane-type Eddy Current Damper[J]. Journal of Hefei University of Technology(Natural Science), 2016, 39(4): 499-502.
[19]	Shi Y, Eberhart R C. Empirical Study of Particle Swarm Optimization[C]//Proceedings of the 1999 Congress on Evolutionary Computation-CEC99. Piscataway: IEEE, 1999: 1945-1950.

参数	参数值
转子直径/m	126
叶片总质量/kg	17 740
机舱质量/kg	240 000
轮廓高度/m	90
轮毂质量/kg	56 780
塔架高度/m	87.6
单桩长度/m	30

迭代次数	RMSE值	迭代次数	RMSE值
10	35.570	40	0.180
20	21.840	50	0.052
30	1.780	60	0.043

系统	SD/m	比率
无控制装置	0.056 3	1
EC-NES	0.053 3	0.947
TMD	0.052 8	0.937